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Class 10MathematicsArithmetic Progressions (AP)Word problems based on APsEasy
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In a shop, the first shelf has (16) boxes and each next shelf has (4) more boxes. How many boxes are there on (9) shelves?

Answer and explanation

Correct answer: 288

The numbers of boxes form an arithmetic progression with first term \(a=16\), common difference \(d=4\), and number of terms \(n=9\).
\(S_9=\frac{9}{2}[2(16)+(9-1)(4)]\)
\(=\frac{9}{2}[32+32]=\frac{9}{2}\times64=288\).
Therefore, the total number of boxes on 9 shelves is 288. Computing only \(16+8\times4=48\) gives the number on the ninth shelf, not the total. Exam tip: when the question asks for a total, use \(S_n\), not \(a_n\).

Related tags

Arithmetic ProgressionAp Word ProblemsSum Of TermsSequence And SeriesClass 10 MathematicsWord Problems Based On ApsArithmetic Progressions (Ap)Arithmetic Progressions Ap
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